This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A242403 #19 Jan 09 2024 08:49:17
%S A242403 2,5,2,6,6,0,2,5,9,0,0,8,8,8,2,9,2,2,1,5,5,0,6,2,7,1,4,3,2,7,8,9,4,1,
%T A242403 4,1,8,2,5,2,1,9,3,3,9,6,2,9,7,8,4,6,1,3,0,1,6,8,6,2,1,7,2,2,9,2,2,8,
%U A242403 0,5,4,8,4,4,7,6,6,3,2,5,6,6,9,5,9,1,4,2,4,4,7,9,3,8,6,8,8,9,4,9
%N A242403 Decimal expansion of the binary self-numbers density constant.
%C A242403 This constant is transcendental (Troi and Zannier, 1999). - _Amiram Eldar_, Nov 28 2020
%D A242403 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 179.
%D A242403 József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.
%D A242403 G. Troi and U. Zannier, Note on the density constant in the distribution of self-numbers, Bollettino dell'Unione Matematica Italiana, Serie 7, Vol. 9-A, No. 1 (1995), pp. 143-148.
%H A242403 G. Troi and U. Zannier, <a href="http://www.bdim.eu/item?id=BUMI_1999_8_2B_2_397_0">Note on the density constant in the distribution of self-numbers - II</a>, Bollettino dell'Unione Matematica Italiana, Serie 8, Vol. 2-B, No. 2 (1999), pp. 397-399; <a href="https://eudml.org/doc/urn:eudml:doc:194654">alternative link</a>.
%H A242403 Umberto Zannier, <a href="https://doi.org/10.1090/S0002-9939-1982-0647887-4">On the distribution of self-numbers</a>, Proc. Amer. Math. Soc., Vol. 85, No. 1 (1982), pp. 10-14.
%H A242403 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A242403 Equals (1/8)*(Sum_{n not a binary self-number} 1/2^n)^2.
%e A242403 0.2526602590088829221550627143278941418252...
%t A242403 m0 = 100; dm = 100; digits = 100; Clear[lambda]; lambda[m_] := lambda[m] = Total[1/2^Union[Table[n + Total[IntegerDigits[n, 2]], {n, 0, m}]]]^2/8 // N[#, 2*digits]& // RealDigits[#, 10, 2*digits]& // First; lambda[m0]; lambda[m = m0 + dm]; While[lambda[m] != lambda[m - dm], Print["m = ", m]; m = m + dm]; lambda[m][[1 ;; digits]]
%Y A242403 Cf. A010061 (binary self numbers), A003052 (decimal self numbers), A010064, A010067, A010070, A092391, A228082.
%K A242403 nonn,cons
%O A242403 0,1
%A A242403 _Jean-François Alcover_, May 13 2014